LINEARLY ORDERED SPACE WHOSE SQUARE AND HIGHER POWERS CANNOT BE CONDENSED ONTO A NORMAL SPACE
2017 ◽
Vol 20
(10)
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pp. 68-73
Keyword(s):
One of the central tasks in the theory of condensations is to describe topological properties that can be improved by condensation (i.e. a continuous one-to-one mapping). Most of the known counterexamples in the field deal with non-hereditary properties. We construct a countably compact linearly ordered (hence, monotonically normal, thus ” very strongly” hereditarily normal) topological space whose square and higher powers cannot be condensed onto a normal space. The constructed space is necessarily pseudocompact in all the powers, which complements a known result on condensations of non-pseudocompact spaces.
1967 ◽
Vol 19
◽
pp. 474-487
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Keyword(s):
1980 ◽
Vol 11
(3)
◽
pp. 281-292
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2001 ◽
Vol 27
(8)
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pp. 505-512
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Keyword(s):
Keyword(s):
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1962 ◽
Vol 14
◽
pp. 461-466
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Keyword(s):
1983 ◽
Vol 26
(4)
◽
pp. 430-437
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